Question

A dilation is applied to △ABC to create △DEF. The side lengths of the two triangles are as follows: AB=6, BC=12, AC=15, DE=8, EF=16, and DF=20. Because the dilation factor is __________, this dilation is a(n) __________.

Answer 1

Answer: The dilation factor is 1.33, this dilation is an enlargement.

Step-by-step explanation:

• A dilation is transformation of figures that creates similar figures but of different sizes.

• It uses dilation factor (k) to either reduce or enlarge the figure.

• When |k| <1 then there is reduction in size of the original figure.

• When |k|>1 then there is enlargement in size of the original figure.

• When |k| =1 then there is no change in size.

Given : A dilation is applied to △ABC to create △DEF.

Since , dilation creates similar figures .

⇒ △ABC≈ △DEF

here , AB corresponds to DE.

BC corresponds to EF.

AC corresponds to DF.

The side-length of corresponding side in image= k x (original length) , where k is dilation factor.

⇒ DE = k (AB)

$\Rightarrow\ k=\dfrac{DE}{AB}=\dfrac{8}{6}=\dfrac{4}{3}=1.33$

Since , the dilation factor 1.33> 1 , therefore it is an enlargement.

Hence, the dilation factor is 1.33, this dilation is an enlargement.